If two roomates sign a year lease and one moves out, it is my understanding that the party who moved out is still legally responsible... correct?

What happens if the one who moves out refuses to pay their share of the rent?

What are the legal rights of the person still residing in the apartment ?

How quickly should they act in taking the other person to court?. could they risk eviction by the landlord in the process of trying to get their money, even though the actions of the other tennat was completely out of their control?

Thank you in advance for your help.

If the lease contains a "joint and several liability" clause, as most do, then the person who remains in the apartment is still responsible for the full amount of the rent and can be evicted if the rent is not paid in full. However the remaining tenant can sue the one who moved out for their share of the rent and utilities until the remaining tenant finds a new roommate to take their place.

You can file a lawsuit against the tenant who moved out at any time, but you can only sue for amounts that were already due. You can't sue for future rent or utilities. So it's in your best interest to find a new roommate immediately and then sue your former roommate after your damages have become a finalized number.